Finite Group Databasebeta

← #17948333

Subgroups — #17948333

Order 4352.

354 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14543704C212yesmaximal, complemented
2#14528695C211yesmaximal, characteristic
3C22⋊#63216—22no—
4C22×#63252C411yescharacteristic
5C2×C22⋊#3622C2211yescharacteristic
6C2×#10587491—22no—
7C2×C17×C22⋊C8C411yescharacteristic
8C23×C4×C17C2×C411yescharacteristic
9C22×C22⋊D17—21no—
10C2×#63252—44no—
11C2×#63252—41no—
12C2×#63252—41no—
13C22×D68C811yescharacteristic
14C22×C4×D17—21no—
15C22×Dic34C811yescharacteristic
16C22×C8×C17—21no—
17C22×#3622D412yes—
18C2×#63216—42no—
19C17×C22⋊C8—41no—
20C22⋊#3622—41no—
21#10587491—44no—
22C24×C17M1611yescharacteristic
23C23×D17—21no—
24C22×C4×C17—21no—
25C22×C4×C17—21no—
26C22×C4×C17—42no—
27C22×C4×C17C22⋊C411yescharacteristic
28C22×C4×C17C2×C811yescharacteristic
29C2×C22⋊D17—42no—
30C2×C22⋊D17—42no—
31C2×C22⋊D17—42no—
32C22×Dic17—21no—
33#63252—44no—
34#63252—44no—
35#63252—44no—
36#63252—44no—
37C2×D68—41no—
38C2×D68—42no—
39C2×C4×D17—24no—
40C2×C4×D17—42no—
41C2×C4×D17—41no—
42C2×C4×D17—41no—
43C2×Dic34—41no—
44C2×Dic34—42no—
45C2×C8×C17—42no—
46C2×C8×C17—41no—
47C2×#3622—22no—
48C2×#3622—42no—
49#63216—82no—
50#7058—171nomaximal, Sylow
51C23×C17—21no—
52C23×C17—22no—
53C23×C17—41no—
54C23×C17—41no—
55C23×C17C22⋊C811yescharacteristic
56C22×D17—22no—
57C22×D17—41no—
58C22×D17—42no—
59C22×D17—41no—
60C22×D17—42no—
61C2×C4×C17—22no—
62C2×C4×C17—21no—
63C2×C4×C17—42no—
64C2×C4×C17—42no—
65C2×C4×C17—41no—
66C2×C4×C17#9911yescharacteristic
67C2×C4×C17#10011yescharacteristic
68C22⋊D17—48no—
69C2×Dic17—22no—
70C2×Dic17—41no—
71C2×Dic17—41no—
72D68—42no—
73D68—42no—
74C4×D17—44no—
75C4×D17—44no—
76Dic34—42no—
77Dic34—42no—
78C8×C17—81no—
79#3622—42no—
80#1780—171no—
81#1314—172no—
82C22×C17—21no—
83C22×C17—21no—
84C22×C17—41no—
85C22×C17—41no—
86C22×C17—41no—
87C22×C17—82no—
88C22×C17#32311yescharacteristic
89C22×C17#35012yes—
90C2×D17—44no—
91C2×D17—42no—
92C2×D17—82no—
93C2×D17—81no—
94C2×D17—81no—
95C4×C17—21no—
96C4×C17—41no—
97C4×C17AΣL(1,𝔽16)12yes—
98Dic17—42no—
99C22×#41—171no—
100C2×C22⋊C8—171no—
101C2×C22⋊C8—342no—
102C2×C22⋊C8#59511yescharacteristic
103C22⋊C16—342no—
104C2×C17—22no—
105C2×C17—81no—
106C2×C17#131511yescharacteristic
107C2×C17#131611yescharacteristic
108C2×C17#132111yescharacteristic
109D17—82no—
110C2×#41—681no—
111C2×#41—681no—
112C2×#41—684no—
113C22×Q8—171no—
114C22×D4—171no—
115C22×D4—341no—
116C23×C4—341no—
117C23×C4C2×#59511yescharacteristic
118C22×C8—21no—
119C22×C8—172no—
120C2×C16—682no—
121C22⋊C8—41no—
122C22⋊C8—684no—
123C22⋊C8—681no—
124C17#705811yescharacteristic, complemented, Sylow
125C24—341no—
126C24#6324311yescharacteristic
127#41—684no—
128#41—684no—
129#41—684no—
130#41—684no—
131C2×Q8—681no—
132C2×Q8—682no—
133C2×D4—681no—
134C2×D4—682no—
135C2×D4—682no—
136C2×D4—682no—
137C2×D4—682no—
138C22×C4—21no—
139C22×C4—21no—
140C22×C4—42no—
141C22×C4—344no—
142C22×C4—341no—
143C22×C4—682no—
144C22×C4—681no—
145C22×C4—681no—
146C22×C4#6324211yescharacteristic
147C22×C4C22⋊#59511yescharacteristic
148C2×C8—42no—
149C2×C8—41no—
150C2×C8—342no—
151C2×C8—682no—
152C16—1362no—
153C23—21no—
154C23—22no—
155C23—41no—
156C23—41no—
157C23—342no—
158C23—681no—
159C23—682no—
160C23—681no—
161C23—682no—
162C23#1058754311yescharacteristic
163Q8—682no—
164Q8—682no—
165D4—682no—
166D4—682no—
167D4—688no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—41no—
173C2×C4—342no—
174C2×C4—684no—
175C2×C4—681no—
176C2×C4—681no—
177C2×C4—684no—
178C2×C4#1058753911yescharacteristic
179C2×C4#1058755311yescharacteristic
180C8—81no—
181C8—682no—
182C22—21no—
183C22—21no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22—82no—
188C22—684no—
189C22—682no—
190C22—1362no—
191C22—1361no—
192C22—1361no—
193C22#1176365311yescharacteristic
194C22#1176370812yes—
195C4—21no—
196C4—41no—
197C4—682no—
198C4#1176371012yes—
199C2—22no—
200C2—81no—
201C2—1362no—
202C2#1454370711yescharacteristic
203C2#1454370911yescharacteristic
204C2#1454371911yescharacteristic
subgroupG/H
centerC2×C4#10587539
commutatorC22×C4×C17C2×C8
FrattiniC23×C4C2×#595
FittingC2×C17×C22⋊C8C4
socleC22×C17#323
prime radicalC22×#63252C4
cosocleC2×C22⋊#3622C22
hypercenterC2×C22⋊C8#595
hypocenterC17#7058
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14543704C2semidirect
124. C17#7058semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145437042
#145286952
#705817